12a
0617
(K12a
0617
)
A knot diagram
1
Linearized knot diagam
3 7 9 1 11 2 6 12 4 5 8 10
Solving Sequence
2,6
7 3
8,11
12 1 5 4 10 9
c
6
c
2
c
7
c
11
c
1
c
5
c
4
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.14855 × 10
164
u
108
+ 9.91104 × 10
164
u
107
+ ··· + 3.18106 × 10
164
b − 5.08463 × 10
164
,
6.17984 × 10
164
u
108
+ 1.13910 × 10
165
u
107
+ ··· + 1.59053 × 10
164
a − 5.91043 × 10
165
, u
109
+ 2u
108
+ ··· − u + 1i
I
u
2
= hu
19
+ u
18
+ ··· + b − 4, −3u
19
+ u
18
+ ··· + a + 7, u
20
− 4u
18
+ ··· − 2u + 1i
I
u
3
= hb − 1, a, u − 1i
I
u
4
= hb
2
− b − 1, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 132 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h4.15 × 10
164
u
108
+ 9.91 × 10
164
u
107
+ · · · + 3.18 × 10
164
b − 5.08 ×
10
164
, 6.18 × 10
164
u
108
+ 1.14 × 10
165
u
107
+ · · · + 1.59 × 10
164
a − 5.91 ×
10
165
, u
109
+ 2u
108
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
−3.88539u
108
− 7.16176u
107
+ ··· + 83.5734u + 37.1601
−1.30414u
108
− 3.11564u
107
+ ··· + 2.90688u + 1.59841
a
12
=
−5.74724u
108
− 12.0466u
107
+ ··· + 79.9400u + 36.7275
−2.82416u
108
− 7.12730u
107
+ ··· + 4.15601u + 3.73114
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−7.34366u
108
− 15.8462u
107
+ ··· + 88.9383u + 26.8680
−6.27613u
108
− 16.6099u
107
+ ··· − 1.72407u + 7.60193
a
4
=
−8.04051u
108
− 17.6315u
107
+ ··· + 89.0488u + 27.8585
−7.00281u
108
− 18.8717u
107
+ ··· − 6.88071u + 8.02606
a
10
=
−12.2999u
108
− 29.7434u
107
+ ··· + 40.7832u + 37.0813
−4.77830u
108
− 12.1689u
107
+ ··· + 10.2999u + 7.68948
a
9
=
0.938066u
108
− 0.178675u
107
+ ··· − 64.8311u − 6.66318
4.49012u
108
+ 12.5916u
107
+ ··· + 9.61880u − 5.02522
(ii) Obstruction class = −1
(iii) Cusp Shapes = 43.5911u
108
+ 118.988u
107
+ ··· + 1.05585u − 49.2425
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
109
+ 32u
108
+ ··· + 55u + 1
c
2
, c
6
u
109
− 2u
108
+ ··· − u − 1
c
3
, c
9
u
109
− u
108
+ ··· + 856u + 293
c
4
u
109
− 2u
108
+ ··· − 108u + 52
c
5
, c
10
u
109
+ u
108
+ ··· + 48996u + 21519
c
8
, c
11
u
109
− u
108
+ ··· + 18267u − 793
c
12
u
109
+ 13u
108
+ ··· − 28u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
109
+ 100y
108
+ ··· + 307y −1
c
2
, c
6
y
109
− 32y
108
+ ··· + 55y −1
c
3
, c
9
y
109
− 53y
108
+ ··· + 1837346y −85849
c
4
y
109
+ 10y
108
+ ··· − 143192y −2704
c
5
, c
10
y
109
− 89y
108
+ ··· + 2877684246y −463067361
c
8
, c
11
y
109
− 97y
108
+ ··· + 200603615y −628849
c
12
y
109
− 15y
108
+ ··· + 66y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.661165 + 0.742727I
a = 0.195427 + 0.540371I
b = 0.020213 − 0.477652I
−0.20374 + 2.40661I 0
u = 0.661165 − 0.742727I
a = 0.195427 − 0.540371I
b = 0.020213 + 0.477652I
−0.20374 − 2.40661I 0
u = −0.976334 + 0.252224I
a = −0.218270 − 0.871137I
b = −0.048014 − 0.939467I
−3.46203 + 7.18678I 0
u = −0.976334 − 0.252224I
a = −0.218270 + 0.871137I
b = −0.048014 + 0.939467I
−3.46203 − 7.18678I 0
u = 1.003040 + 0.144402I
a = −1.20964 + 0.87778I
b = −1.199990 − 0.023868I
3.47317 − 0.24757I 0
u = 1.003040 − 0.144402I
a = −1.20964 − 0.87778I
b = −1.199990 + 0.023868I
3.47317 + 0.24757I 0
u = −0.905223 + 0.388324I
a = −0.02277 + 2.13503I
b = 1.141670 − 0.019481I
1.72496 + 4.25483I 0
u = −0.905223 − 0.388324I
a = −0.02277 − 2.13503I
b = 1.141670 + 0.019481I
1.72496 − 4.25483I 0
u = −1.01750
a = 1.13768
b = −0.284524
−0.463998 0
u = −1.014120 + 0.084818I
a = −0.516516 + 0.665731I
b = −0.130858 + 0.716290I
−5.83774 + 2.31727I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014120 − 0.084818I
a = −0.516516 − 0.665731I
b = −0.130858 − 0.716290I
−5.83774 − 2.31727I 0
u = 0.030596 + 0.980436I
a = 1.44950 + 0.15540I
b = −1.40520 − 0.18421I
5.03215 + 7.06267I 0
u = 0.030596 − 0.980436I
a = 1.44950 − 0.15540I
b = −1.40520 + 0.18421I
5.03215 − 7.06267I 0
u = 0.938705 + 0.234216I
a = 1.00187 + 1.50437I
b = −1.159070 + 0.428276I
−2.74477 − 6.50226I 0
u = 0.938705 − 0.234216I
a = 1.00187 − 1.50437I
b = −1.159070 − 0.428276I
−2.74477 + 6.50226I 0
u = 1.000280 + 0.373320I
a = −1.171100 + 0.055335I
b = 0.286618 − 0.275036I
−2.85087 + 1.37002I 0
u = 1.000280 − 0.373320I
a = −1.171100 − 0.055335I
b = 0.286618 + 0.275036I
−2.85087 − 1.37002I 0
u = −0.826944 + 0.398766I
a = −0.99871 + 1.45976I
b = 0.954266 + 0.392428I
0.20457 + 3.66147I 0
u = −0.826944 − 0.398766I
a = −0.99871 − 1.45976I
b = 0.954266 − 0.392428I
0.20457 − 3.66147I 0
u = −1.000340 + 0.412185I
a = 0.207654 − 0.224164I
b = −0.988621 + 0.492926I
−1.76783 − 1.01134I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.000340 − 0.412185I
a = 0.207654 + 0.224164I
b = −0.988621 − 0.492926I
−1.76783 + 1.01134I 0
u = 0.960169 + 0.508207I
a = 0.842050 + 0.711747I
b = −0.402772 + 0.665401I
−3.41610 − 3.37548I 0
u = 0.960169 − 0.508207I
a = 0.842050 − 0.711747I
b = −0.402772 − 0.665401I
−3.41610 + 3.37548I 0
u = −0.858846 + 0.694130I
a = 0.508624 + 0.649041I
b = 0.048170 − 0.665084I
2.60155 + 2.66611I 0
u = −0.858846 − 0.694130I
a = 0.508624 − 0.649041I
b = 0.048170 + 0.665084I
2.60155 − 2.66611I 0
u = −0.799149 + 0.781766I
a = 2.19590 − 0.45743I
b = −1.44513 − 0.32787I
3.81951 + 0.94067I 0
u = −0.799149 − 0.781766I
a = 2.19590 + 0.45743I
b = −1.44513 + 0.32787I
3.81951 − 0.94067I 0
u = −1.059690 + 0.358007I
a = −0.038766 − 1.274390I
b = −1.352230 − 0.381056I
4.74029 + 6.33732I 0
u = −1.059690 − 0.358007I
a = −0.038766 + 1.274390I
b = −1.352230 + 0.381056I
4.74029 − 6.33732I 0
u = 0.803376 + 0.807377I
a = −0.528767 − 0.357828I
b = −0.131242 − 0.659880I
5.32098 − 1.05831I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803376 − 0.807377I
a = −0.528767 + 0.357828I
b = −0.131242 + 0.659880I
5.32098 + 1.05831I 0
u = −0.830444 + 0.797738I
a = −1.58731 − 0.18078I
b = 1.367240 − 0.252886I
9.36477 + 1.39425I 0
u = −0.830444 − 0.797738I
a = −1.58731 + 0.18078I
b = 1.367240 + 0.252886I
9.36477 − 1.39425I 0
u = 0.836899 + 0.122080I
a = 1.30312 − 1.30535I
b = 1.48765 − 1.06513I
0.182204 − 0.255174I 0
u = 0.836899 − 0.122080I
a = 1.30312 + 1.30535I
b = 1.48765 + 1.06513I
0.182204 + 0.255174I 0
u = 0.803929 + 0.835678I
a = 0.330209 − 0.714142I
b = 0.474741 + 1.283770I
3.52710 + 5.55369I 0
u = 0.803929 − 0.835678I
a = 0.330209 + 0.714142I
b = 0.474741 − 1.283770I
3.52710 − 5.55369I 0
u = −0.823089 + 0.828104I
a = −2.37812 + 0.90318I
b = 1.326080 − 0.143246I
3.96993 − 4.50077I 0
u = −0.823089 − 0.828104I
a = −2.37812 − 0.90318I
b = 1.326080 + 0.143246I
3.96993 + 4.50077I 0
u = −0.867552 + 0.788920I
a = 0.07285 − 1.80338I
b = −1.35517 + 1.82595I
5.49744 + 2.55035I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.867552 − 0.788920I
a = 0.07285 + 1.80338I
b = −1.35517 − 1.82595I
5.49744 − 2.55035I 0
u = −0.660985 + 0.988388I
a = −1.368010 + 0.150443I
b = 1.40381 − 0.21039I
10.41470 − 2.04001I 0
u = −0.660985 − 0.988388I
a = −1.368010 − 0.150443I
b = 1.40381 + 0.21039I
10.41470 + 2.04001I 0
u = −0.152507 + 0.790804I
a = −1.367890 + 0.290651I
b = 1.43084 − 0.17609I
7.76885 − 2.34135I 0
u = −0.152507 − 0.790804I
a = −1.367890 − 0.290651I
b = 1.43084 + 0.17609I
7.76885 + 2.34135I 0
u = −0.907115 + 0.777894I
a = −2.40586 + 0.08420I
b = 1.29801 + 1.84173I
5.37410 + 3.34707I 0
u = −0.907115 − 0.777894I
a = −2.40586 − 0.08420I
b = 1.29801 − 1.84173I
5.37410 − 3.34707I 0
u = 0.785186 + 0.904351I
a = −1.63676 − 0.60027I
b = 1.65977 + 0.48170I
13.13880 + 5.17289I 0
u = 0.785186 − 0.904351I
a = −1.63676 + 0.60027I
b = 1.65977 − 0.48170I
13.13880 − 5.17289I 0
u = 0.997125 + 0.679627I
a = −0.882367 + 0.217636I
b = 0.075534 − 0.535629I
−1.20586 − 7.83499I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997125 − 0.679627I
a = −0.882367 − 0.217636I
b = 0.075534 + 0.535629I
−1.20586 + 7.83499I 0
u = 0.885220 + 0.832751I
a = 1.92957 + 0.89808I
b = −1.361340 − 0.152144I
7.36684 − 0.19643I 0
u = 0.885220 − 0.832751I
a = 1.92957 − 0.89808I
b = −1.361340 + 0.152144I
7.36684 + 0.19643I 0
u = −0.753469 + 0.954538I
a = 1.62545 − 0.42562I
b = −1.57315 + 0.44747I
10.0462 − 11.6265I 0
u = −0.753469 − 0.954538I
a = 1.62545 + 0.42562I
b = −1.57315 − 0.44747I
10.0462 + 11.6265I 0
u = −0.958887 + 0.748825I
a = −1.52024 + 1.38193I
b = 1.44205 − 0.14285I
3.32664 + 4.84834I 0
u = −0.958887 − 0.748825I
a = −1.52024 − 1.38193I
b = 1.44205 + 0.14285I
3.32664 − 4.84834I 0
u = −0.941747 + 0.770309I
a = 1.46084 − 1.90678I
b = −1.292380 − 0.282727I
9.02024 + 4.50855I 0
u = −0.941747 − 0.770309I
a = 1.46084 + 1.90678I
b = −1.292380 + 0.282727I
9.02024 − 4.50855I 0
u = 0.849900 + 0.872637I
a = 1.81852 + 0.00530I
b = −1.350050 − 0.223970I
9.66398 + 1.44155I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.849900 − 0.872637I
a = 1.81852 − 0.00530I
b = −1.350050 + 0.223970I
9.66398 − 1.44155I 0
u = −0.878995 + 0.850021I
a = 0.535980 − 0.185923I
b = 0.091462 − 0.615375I
5.39001 + 4.55531I 0
u = −0.878995 − 0.850021I
a = 0.535980 + 0.185923I
b = 0.091462 + 0.615375I
5.39001 − 4.55531I 0
u = 0.913156 + 0.825065I
a = −2.11779 − 0.87152I
b = 1.381070 − 0.248120I
7.28142 − 5.98080I 0
u = 0.913156 − 0.825065I
a = −2.11779 + 0.87152I
b = 1.381070 + 0.248120I
7.28142 + 5.98080I 0
u = 0.964405 + 0.765387I
a = −0.168809 − 0.324984I
b = −0.028739 − 0.713563I
4.82272 − 4.85805I 0
u = 0.964405 − 0.765387I
a = −0.168809 + 0.324984I
b = −0.028739 + 0.713563I
4.82272 + 4.85805I 0
u = −0.955783 + 0.787070I
a = 2.35933 − 0.99223I
b = −1.374010 − 0.211633I
3.55812 + 10.54490I 0
u = −0.955783 − 0.787070I
a = 2.35933 + 0.99223I
b = −1.374010 + 0.211633I
3.55812 − 10.54490I 0
u = −0.926398 + 0.832788I
a = 0.181087 − 0.141302I
b = 0.011496 − 0.664221I
5.24216 + 1.69899I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926398 − 0.832788I
a = 0.181087 + 0.141302I
b = 0.011496 + 0.664221I
5.24216 − 1.69899I 0
u = 0.969659 + 0.783750I
a = 1.186520 − 0.050474I
b = −0.369041 + 1.351730I
3.01438 − 11.60760I 0
u = 0.969659 − 0.783750I
a = 1.186520 + 0.050474I
b = −0.369041 − 1.351730I
3.01438 + 11.60760I 0
u = 0.740769 + 0.123273I
a = 0.464865 + 0.234971I
b = 0.489198 + 0.364767I
−1.161380 − 0.158674I −9.36316 + 0.I
u = 0.740769 − 0.123273I
a = 0.464865 − 0.234971I
b = 0.489198 − 0.364767I
−1.161380 + 0.158674I −9.36316 + 0.I
u = 1.196090 + 0.360754I
a = −0.201276 − 1.003410I
b = 1.352590 − 0.348516I
1.00912 − 11.66170I 0
u = 1.196090 − 0.360754I
a = −0.201276 + 1.003410I
b = 1.352590 + 0.348516I
1.00912 + 11.66170I 0
u = 0.961642 + 0.827717I
a = −1.83141 − 1.63588I
b = 1.311060 − 0.257851I
9.31141 − 7.75148I 0
u = 0.961642 − 0.827717I
a = −1.83141 + 1.63588I
b = 1.311060 + 0.257851I
9.31141 + 7.75148I 0
u = 0.808053 + 1.005860I
a = 1.43540 + 0.26996I
b = −1.390190 − 0.199565I
10.29570 − 1.65032I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808053 − 1.005860I
a = 1.43540 − 0.26996I
b = −1.390190 + 0.199565I
10.29570 + 1.65032I 0
u = 1.010470 + 0.808639I
a = 1.84396 + 1.37838I
b = −1.64199 + 0.55881I
12.4282 − 11.5053I 0
u = 1.010470 − 0.808639I
a = 1.84396 − 1.37838I
b = −1.64199 − 0.55881I
12.4282 + 11.5053I 0
u = 1.32214
a = −0.235795
b = −1.26721
2.76277 0
u = 0.664276 + 0.109625I
a = −0.12102 − 1.76636I
b = −1.00911 − 1.32316I
0.671854 − 0.543097I 12.7069 − 20.8624I
u = 0.664276 − 0.109625I
a = −0.12102 + 1.76636I
b = −1.00911 + 1.32316I
0.671854 + 0.543097I 12.7069 + 20.8624I
u = −1.049790 + 0.814406I
a = −1.73565 + 1.37041I
b = 1.56386 + 0.51012I
9.1037 + 18.1194I 0
u = −1.049790 − 0.814406I
a = −1.73565 − 1.37041I
b = 1.56386 − 0.51012I
9.1037 − 18.1194I 0
u = −1.306190 + 0.300163I
a = 0.003658 + 0.585361I
b = 1.268940 − 0.067403I
0.38996 − 2.48227I 0
u = −1.306190 − 0.300163I
a = 0.003658 − 0.585361I
b = 1.268940 + 0.067403I
0.38996 + 2.48227I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328002 + 0.562591I
a = −0.014485 − 0.398339I
b = 0.278009 + 0.578098I
−1.76193 − 0.69910I −3.72710 + 0.40694I
u = 0.328002 − 0.562591I
a = −0.014485 + 0.398339I
b = 0.278009 − 0.578098I
−1.76193 + 0.69910I −3.72710 − 0.40694I
u = −0.333528 + 0.552545I
a = 2.17032 + 0.30515I
b = −1.398850 − 0.045827I
3.48691 − 0.72395I 2.18612 − 0.71861I
u = −0.333528 − 0.552545I
a = 2.17032 − 0.30515I
b = −1.398850 + 0.045827I
3.48691 + 0.72395I 2.18612 + 0.71861I
u = 1.043740 + 0.881657I
a = −1.45373 − 1.09184I
b = 1.345900 − 0.286525I
9.54338 − 5.20763I 0
u = 1.043740 − 0.881657I
a = −1.45373 + 1.09184I
b = 1.345900 + 0.286525I
9.54338 + 5.20763I 0
u = −1.109850 + 0.800965I
a = 1.17004 − 1.21199I
b = −1.336920 − 0.304212I
9.02417 + 8.57896I 0
u = −1.109850 − 0.800965I
a = 1.17004 + 1.21199I
b = −1.336920 + 0.304212I
9.02417 − 8.57896I 0
u = −0.418261 + 0.453237I
a = −1.96959 + 1.66953I
b = 0.977043 + 0.528463I
0.04799 + 4.72568I 2.25367 − 4.11714I
u = −0.418261 − 0.453237I
a = −1.96959 − 1.66953I
b = 0.977043 − 0.528463I
0.04799 − 4.72568I 2.25367 + 4.11714I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606220
a = −3.01282
b = 1.43104
5.28454 −10.6430
u = −0.365739 + 0.332574I
a = 1.93085 − 1.18009I
b = −0.804586 + 0.142577I
1.42084 − 0.59712I 4.39475 + 0.33799I
u = −0.365739 − 0.332574I
a = 1.93085 + 1.18009I
b = −0.804586 − 0.142577I
1.42084 + 0.59712I 4.39475 − 0.33799I
u = 0.113491 + 0.448845I
a = 1.77694 + 0.91984I
b = 0.384609 − 0.417184I
−0.52625 − 4.68055I −0.31458 + 5.32328I
u = 0.113491 − 0.448845I
a = 1.77694 − 0.91984I
b = 0.384609 + 0.417184I
−0.52625 + 4.68055I −0.31458 − 5.32328I
u = −0.329231 + 0.097875I
a = 1.98377 + 2.48287I
b = −0.527899 − 0.109148I
1.41436 + 0.46555I 7.20348 − 0.07782I
u = −0.329231 − 0.097875I
a = 1.98377 − 2.48287I
b = −0.527899 + 0.109148I
1.41436 − 0.46555I 7.20348 + 0.07782I
u = 0.285434 + 0.027526I
a = 0.03601 − 6.35580I
b = 0.764995 + 0.255245I
−0.38421 + 4.63897I −2.39558 − 3.93267I
u = 0.285434 − 0.027526I
a = 0.03601 + 6.35580I
b = 0.764995 − 0.255245I
−0.38421 − 4.63897I −2.39558 + 3.93267I
15
II.
I
u
2
= hu
19
+u
18
+· · ·+b−4, −3u
19
+u
18
+· · ·+a+7, u
20
−4u
18
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
3u
19
− u
18
+ ··· − 7u − 7
−u
19
− u
18
+ ··· − 2u + 4
a
12
=
2u
19
− u
18
+ ··· − 4u − 5
−u
19
− u
18
+ ··· − u + 4
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
4u
19
+ 3u
18
+ ··· − u − 8
−u
19
+ 4u
17
+ ··· + 4u + 2
a
4
=
3u
19
+ 3u
18
+ ··· − 2u − 7
−2u
19
− u
18
+ ··· + 5u + 3
a
10
=
−3u
19
− 3u
18
+ ··· − 4u + 7
2u
19
− 7u
17
+ ··· − 3u − 1
a
9
=
−5u
19
− 2u
18
+ ··· − 56u
2
+ 13
3u
19
+ u
18
+ ··· − u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −21u
19
− 11u
18
+ 77u
17
+ 84u
16
− 202u
15
− 238u
14
+ 339u
13
+ 528u
12
− 433u
11
−
799u
10
+ 367u
9
+ 931u
8
− 206u
7
− 784u
6
+ 40u
5
+ 466u
4
+ 40u
3
− 168u
2
− 8u + 34
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 14u + 1
c
2
u
20
− 4u
18
+ ··· + 2u + 1
c
3
u
20
− 2u
18
+ ··· + 4u
2
− 1
c
4
u
20
+ 3u
19
+ ··· − 25u − 5
c
5
u
20
− 4u
18
+ ··· + 2u
2
− 1
c
6
u
20
− 4u
18
+ ··· − 2u + 1
c
7
u
20
+ 8u
19
+ ··· + 14u + 1
c
8
u
20
− 8u
19
+ ··· − 4u + 1
c
9
u
20
− 2u
18
+ ··· + 4u
2
− 1
c
10
u
20
− 4u
18
+ ··· + 2u
2
− 1
c
11
u
20
+ 8u
19
+ ··· + 4u + 1
c
12
u
20
− 4u
19
+ ··· − 12u + 1
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 16y
19
+ ··· − 22y + 1
c
2
, c
6
y
20
− 8y
19
+ ··· − 14y + 1
c
3
, c
9
y
20
− 4y
19
+ ··· − 8y + 1
c
4
y
20
+ y
19
+ ··· + 15y + 25
c
5
, c
10
y
20
− 8y
19
+ ··· − 4y + 1
c
8
, c
11
y
20
− 20y
19
+ ··· − 8y + 1
c
12
y
20
− 6y
19
+ ··· − 24y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728618 + 0.611457I
a = −0.50308 − 1.36076I
b = −0.707461 + 0.383094I
0.68545 − 3.45384I 1.05823 + 2.65940I
u = −0.728618 − 0.611457I
a = −0.50308 + 1.36076I
b = −0.707461 − 0.383094I
0.68545 + 3.45384I 1.05823 − 2.65940I
u = 0.859847 + 0.664460I
a = 0.850334 − 1.113260I
b = −0.029313 + 0.797315I
3.13994 − 2.57396I 11.64294 + 3.03636I
u = 0.859847 − 0.664460I
a = 0.850334 + 1.113260I
b = −0.029313 − 0.797315I
3.13994 + 2.57396I 11.64294 − 3.03636I
u = 1.053280 + 0.321186I
a = −0.805082 − 0.480764I
b = 0.852892 + 0.263674I
−2.03747 + 2.49614I −3.26688 − 5.12322I
u = 1.053280 − 0.321186I
a = −0.805082 + 0.480764I
b = 0.852892 − 0.263674I
−2.03747 − 2.49614I −3.26688 + 5.12322I
u = −0.974683 + 0.605885I
a = −0.505808 − 0.144583I
b = 0.694162 + 0.315826I
−0.10942 + 8.27031I 0.82347 − 8.04504I
u = −0.974683 − 0.605885I
a = −0.505808 + 0.144583I
b = 0.694162 − 0.315826I
−0.10942 − 8.27031I 0.82347 + 8.04504I
u = −0.794716 + 0.899725I
a = −1.51174 − 0.06899I
b = 1.309590 − 0.209101I
9.45777 − 0.46305I 2.26958 − 1.89503I
u = −0.794716 − 0.899725I
a = −1.51174 + 0.06899I
b = 1.309590 + 0.209101I
9.45777 + 0.46305I 2.26958 + 1.89503I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.894870 + 0.803962I
a = −0.701199 + 0.176411I
b = −0.022957 − 1.138260I
5.82936 − 3.01398I 1.54320 + 2.64580I
u = 0.894870 − 0.803962I
a = −0.701199 − 0.176411I
b = −0.022957 + 1.138260I
5.82936 + 3.01398I 1.54320 − 2.64580I
u = −0.753583 + 0.142607I
a = 0.71080 + 1.30459I
b = −0.075777 + 0.956686I
0.376061 + 0.589442I −2.89294 + 2.96900I
u = −0.753583 − 0.142607I
a = 0.71080 − 1.30459I
b = −0.075777 − 0.956686I
0.376061 − 0.589442I −2.89294 − 2.96900I
u = 1.23437
a = −0.541146
b = −1.20687
2.12941 −5.93270
u = 0.618967 + 0.364095I
a = 1.38714 + 3.06211I
b = −0.859186 + 0.407319I
−0.40553 − 5.47295I −3.49503 + 13.06566I
u = 0.618967 − 0.364095I
a = 1.38714 − 3.06211I
b = −0.859186 − 0.407319I
−0.40553 + 5.47295I −3.49503 − 13.06566I
u = −1.010830 + 0.835159I
a = 1.47623 − 1.41537I
b = −1.254460 − 0.261696I
8.80052 + 6.87719I 0.50911 − 3.15662I
u = −1.010830 − 0.835159I
a = 1.47623 + 1.41537I
b = −1.254460 + 0.261696I
8.80052 − 6.87719I 0.50911 + 3.15662I
u = 0.436549
a = −4.25403
b = 1.39188
5.61485 14.5490
22
III. I
u
3
= hb − 1, a, u − 1i
(i) Arc colorings
a
2
=
0
1
a
6
=
1
0
a
7
=
1
1
a
3
=
−1
0
a
8
=
0
1
a
11
=
0
1
a
12
=
0
1
a
1
=
1
1
a
5
=
1
1
a
4
=
1
1
a
10
=
−1
0
a
9
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
9
, c
10
u + 1
c
4
, c
8
, c
11
u
c
12
u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
9
, c
10
, c
12
y −1
c
4
, c
8
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
26
IV. I
u
4
= hb
2
− b − 1, a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
8
=
0
1
a
11
=
1
b
a
12
=
1
b − 1
a
1
=
−1
−1
a
5
=
b + 1
b + 1
a
4
=
b + 1
b + 1
a
10
=
−2b
−b − 1
a
9
=
1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u − 1)
2
c
3
, c
5
, c
12
u
2
− u − 1
c
4
u
2
c
6
, c
7
, c
8
(u + 1)
2
c
9
, c
10
u
2
+ u − 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
(y −1)
2
c
3
, c
5
, c
9
c
10
, c
12
y
2
− 3y + 1
c
4
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −0.618034
0 5.00000
u = −1.00000
a = 1.00000
b = 1.61803
0 5.00000
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u + 1)(u
20
− 8u
19
+ ··· − 14u + 1)
· (u
109
+ 32u
108
+ ··· + 55u + 1)
c
2
((u − 1)
2
)(u + 1)(u
20
− 4u
18
+ ··· + 2u + 1)(u
109
− 2u
108
+ ··· − u − 1)
c
3
(u + 1)(u
2
− u − 1)(u
20
− 2u
18
+ ··· + 4u
2
− 1)
· (u
109
− u
108
+ ··· + 856u + 293)
c
4
u
3
(u
20
+ 3u
19
+ ··· − 25u − 5)(u
109
− 2u
108
+ ··· − 108u + 52)
c
5
(u + 1)(u
2
− u − 1)(u
20
− 4u
18
+ ··· + 2u
2
− 1)
· (u
109
+ u
108
+ ··· + 48996u + 21519)
c
6
((u + 1)
3
)(u
20
− 4u
18
+ ··· − 2u + 1)(u
109
− 2u
108
+ ··· − u − 1)
c
7
((u + 1)
3
)(u
20
+ 8u
19
+ ··· + 14u + 1)(u
109
+ 32u
108
+ ··· + 55u + 1)
c
8
u(u + 1)
2
(u
20
− 8u
19
+ ··· − 4u + 1)(u
109
− u
108
+ ··· + 18267u − 793)
c
9
(u + 1)(u
2
+ u − 1)(u
20
− 2u
18
+ ··· + 4u
2
− 1)
· (u
109
− u
108
+ ··· + 856u + 293)
c
10
(u + 1)(u
2
+ u − 1)(u
20
− 4u
18
+ ··· + 2u
2
− 1)
· (u
109
+ u
108
+ ··· + 48996u + 21519)
c
11
u(u − 1)
2
(u
20
+ 8u
19
+ ··· + 4u + 1)(u
109
− u
108
+ ··· + 18267u − 793)
c
12
(u − 1)(u
2
− u − 1)(u
20
− 4u
19
+ ··· − 12u + 1)
· (u
109
+ 13u
108
+ ··· − 28u − 1)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y −1)
3
)(y
20
+ 16y
19
+ ··· − 22y + 1)(y
109
+ 100y
108
+ ··· + 307y −1)
c
2
, c
6
((y −1)
3
)(y
20
− 8y
19
+ ··· − 14y + 1)(y
109
− 32y
108
+ ··· + 55y −1)
c
3
, c
9
(y −1)(y
2
− 3y + 1)(y
20
− 4y
19
+ ··· − 8y + 1)
· (y
109
− 53y
108
+ ··· + 1837346y −85849)
c
4
y
3
(y
20
+ y
19
+ ··· + 15y + 25)(y
109
+ 10y
108
+ ··· − 143192y −2704)
c
5
, c
10
(y −1)(y
2
− 3y + 1)(y
20
− 8y
19
+ ··· − 4y + 1)
· (y
109
− 89y
108
+ ··· + 2877684246y −463067361)
c
8
, c
11
y(y −1)
2
(y
20
− 20y
19
+ ··· − 8y + 1)
· (y
109
− 97y
108
+ ··· + 200603615y −628849)
c
12
(y −1)(y
2
− 3y + 1)(y
20
− 6y
19
+ ··· − 24y + 1)
· (y
109
− 15y
108
+ ··· + 66y −1)
32
